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True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity Formula

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True Anomaly in Elliptical Orbit measures the angle between the object's current position and the perigee (the point of closest approach to the central body) when viewed from the focus of the orbit. Check FAQs

θ e = 2 \cdot a \tan (\sqrt{\frac{1 + e e}{1 - e e}} \cdot \tan (\frac{E}{2}))

θ_e - True Anomaly in Elliptical Orbit?e_e - Eccentricity of Elliptical Orbit?E - Eccentric Anomaly?

True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity Example

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Here is how the True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity equation looks like with Values.

Here is how the True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity equation looks like with Units.

Here is how the True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity equation looks like.

135.1097 = 2 \cdot a \tan (\sqrt{\frac{1 + 0.6}{1 - 0.6}} \cdot \tan (\frac{100.874}{2}))

135.1097° = 2 \cdot a \tan (\sqrt{\frac{1 + 0.6}{1 - 0.6}} \cdot \tan (\frac{100.874°}{2}))

135.1097 = 2 \cdot a \tan (\sqrt{\frac{1 + 0.6}{1 - 0.6}} \cdot \tan (\frac{100.874}{2}))

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True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity Solution

Follow our step by step solution on how to calculate True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity?

FIRST Step Consider the formula

θ e = 2 \cdot a \tan (\sqrt{\frac{1 + e e}{1 - e e}} \cdot \tan (\frac{E}{2}))

Next Step Substitute values of Variables

∴

θ e = 2 \cdot a \tan (\sqrt{\frac{1 + 0.6}{1 - 0.6}} \cdot \tan (\frac{100.874°}{2}))

Next Step Convert Units

∴

θ e = 2 \cdot a \tan (\sqrt{\frac{1 + 0.6}{1 - 0.6}} \cdot \tan (\frac{1.7606rad}{2}))

Next Step Prepare to Evaluate

∴

θ e = 2 \cdot a \tan (\sqrt{\frac{1 + 0.6}{1 - 0.6}} \cdot \tan (\frac{1.7606}{2}))

Next Step Evaluate

∴

θ e = 2.35810919059733rad

Next Step Convert to Output's Unit

∴

θ e = 135.109704252263°

LAST Step Rounding Answer

∴

θ e = 135.1097°

True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity Formula Elements

Variables

Functions

True Anomaly in Elliptical Orbit

True Anomaly in Elliptical Orbit measures the angle between the object's current position and the perigee (the point of closest approach to the central body) when viewed from the focus of the orbit.

Symbol: θ_e

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find True Anomaly in Elliptical Orbit

Eccentricity of Elliptical Orbit

Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is.

Symbol: e_e

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Eccentricity of Elliptical Orbit

Eccentric Anomaly

The Eccentric Anomaly is an angular parameter that defines the position of a body that is moving along an Kepler orbit.

Symbol: E

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Eccentric Anomaly

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

atan

Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle.

Syntax: atan(Number)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Orbital Position as Function of Time category

Go Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity

E = 2 \cdot a \tan (\sqrt{\frac{1 - e e}{1 + e e}} \cdot \tan (\frac{θ e}{2}))

Go Mean Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity

M e = E - e e \cdot \sin (E)

Go Time since Periapsis in Elliptic Orbit given Mean Anomaly

t e = M e \cdot \frac{T e}{2 \cdot π}

Go Time since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period

t e = (E - e e \cdot \sin (E)) \cdot \frac{T e}{2 \cdot Π (6)}

How to Evaluate True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity?

True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity evaluator uses True Anomaly in Elliptical Orbit = 2*atan(sqrt((1+Eccentricity of Elliptical Orbit)/(1-Eccentricity of Elliptical Orbit))*tan(Eccentric Anomaly/2)) to evaluate the True Anomaly in Elliptical Orbit, True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity formula is defined as a measure of the angle between the current position of an object in its elliptical orbit and the point of closest approach to the central body. True Anomaly in Elliptical Orbit is denoted by θ_e symbol.

How to evaluate True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity using this online evaluator? To use this online evaluator for True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity, enter Eccentricity of Elliptical Orbit (e_e) & Eccentric Anomaly (E) and hit the calculate button.

FAQs on True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity

What is the formula to find True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity?

The formula of True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity is expressed as True Anomaly in Elliptical Orbit = 2*atan(sqrt((1+Eccentricity of Elliptical Orbit)/(1-Eccentricity of Elliptical Orbit))*tan(Eccentric Anomaly/2)). Here is an example- 7746.401 = 2*atan(sqrt((1+0.6)/(1-0.6))*tan(1.76058342965643/2)).

How to calculate True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity?

With Eccentricity of Elliptical Orbit (e_e) & Eccentric Anomaly (E) we can find True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity using the formula - True Anomaly in Elliptical Orbit = 2*atan(sqrt((1+Eccentricity of Elliptical Orbit)/(1-Eccentricity of Elliptical Orbit))*tan(Eccentric Anomaly/2)). This formula also uses Tangent (tan)Inverse Tan (atan), Square Root (sqrt) function(s).

Can the True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity be negative?

Yes, the True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity, measured in Angle can be negative.

Which unit is used to measure True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity?

True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity can be measured.

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